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# Math problem

Sat 25 Jul, 2009 05:15 am
http://i26.tinypic.com/28aui5w.jpg
How many time you can read the word LOGIGRILLES in the image,knowing that each letter is linked up with two letters below and two letters above.
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Type: Question • Score: 0 • Views: 2,222 • Replies: 8
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rohtarantula

1
Sat 25 Jul, 2009 05:25 am
@rohtarantula,
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fresco

1
Sat 25 Jul, 2009 11:48 am
@rohtarantula,
The answer is exactly 200. (Variation on Pascal's Triangle)
oolongteasup

1
Sun 26 Jul, 2009 01:23 am
@fresco,
I get 32.
fresco

1
Sun 26 Jul, 2009 02:38 am
@oolongteasup,
The problem is typical of a "how many routes through a road network without going back on yourself" problem. Each letter is a road junction with a left/right decision. The solution is found by cummulatively summing the possible routes to each junction as you go. For example the first three G's have value 1,2,1 respectively, which then gives the four I's as 1,3,3,1. The next line of G's will therefore be 4,6,4 and so on. (Check out Pascal's Triangle).
oolongteasup

1
Sun 26 Jul, 2009 04:42 am
@fresco,
Yes well that explains it, now I get 33.
fresco

1
Sun 26 Jul, 2009 08:09 am
@oolongteasup,

L=1
OO=1,1
GGG=1,2,1
IIII=1,3,3,1
GGG=4,6,4
RR=10,10
III=10,20,10
LLLL=10,30,30,10
LLL=40,60,40
EE=100,100
S=200

Each number is the sum of the preceding left and right "ears" above it.
fresco

1
Sun 26 Jul, 2009 08:26 am
@fresco,
...for example the first GGG = 1,2,1 because there is only one path to the outer G's but two to the middle one. Similarly, the line below is 1,3,3,1 because the second and third I's can be reached by 1+2 =3 ways from the G's above them, whereas the outer I's can only be reached by the single path G above them.
oolongteasup

1
Mon 27 Jul, 2009 09:55 pm
@fresco,
Good work fresco and thanks for the derivation of the answer.
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